Several injured Texans players are still day-to-day after sitting out of Sunday's game at Tennessee.
Texans coach Gary Kubiak said Monday that cornerback Johnathan Joseph, who has hamstring and groin injuries and has missed the last two games, is "doing well" and ran on Monday. Joseph's return would be especially important this week with the Texans facing Tom Brady and the New England Patriots, cornerback Brice McCain going on injured reserve and cornerback Alan Ball day-to-day with a foot injury.
Joseph, Ball, right tackle Derek Newton (knee), inside linebacker Bradie James (hamstring) and guard Antoine Caldwell (hamstring) will all be evaluated as the week progresses. Outside linebacker Brooks Reed (groin) will be out for at least another couple of weeks.
"They're all making progress," Kubiak said on Monday. "I think they're all going to be a day-to-day process right now and then probably end-of-the-week decisions for us as a football team, but Brooks is still the one that has a ways to go."
Aside from McCain, tight end Garrett Graham suffered the Texans' most significant injury against the Titans. Graham left the game with a concussion and will have to pass league testing procedures this week in order to get clearance to play at New England.
"Garrett has taken step one already today," Kubiak said. "He's doing much better. He was doing much better on the plane ride home. He has a four-, five-step phase as far as making it back from the concussion protocol. He's through step one today and doing much better."
Texans left tackle Duane Brown is OK after an injury scare on Sunday. Brown left the game in the first quarter after taking a shot to his left knee but returned to the field four plays later.
"Duane is fine," Kubiak said. "Duane just came out of the game with a bruised knee. He's feeling fine today. All tests came out OK, so we're moving forward and very lucky with Duane."
The Texans will get back to practice on Thursday because of their upcoming Monday night game in Foxboro. The extra day off could help Joseph, James and some of the other players have a better chance of returning for a game that could ultimately decide the top seed in the AFC playoffs.